All Students should be aware that the Department of Mathematical Sciences takes the NJIT Honor code very seriously and enforces it strictly. This means there must not be any forms of plagiarism, i.e., copying of homework, class projects, or lab assignments, or any form of cheating in quizzes and exams. Under the Honor Code, students are obligated to report any such activities to the Instructor.
Mathematics 222-004:
differential equations
Spring 2007
Instructor: Prof.
Rotstein
Textbook: Elementary
Differential Equations and Boundary Value Problems, 8th Ed., by Boyce and DiPrima
Grading Policy: The final grade in this course will
be determined as follows:
|
☑ Homework + Quizzes: |
|
17% |
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☑ 3 Common Exams: |
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51% |
|
☑ Final Exam: |
|
32% |
A
final average grade of 60
is required to pass
this class. A final average grade of 85
is required to earn a grade of A.
Please
note that the University Drop Date March
26, 2007
deadline will be strictly enforced.
Homework & Quiz
Policy: Homework
Assignments chosen from the text are attached to this document. Students are required to work through these
problems after each lecture in order to gain a better understanding of the course
material. Weekly quizzes will be based
on these exercises.
MATLAB: MATLAB is a mathematical software
program that is used throughout the science and engineering curriculum. Several
MATLAB assignments will be given out. These assignments have been designed to
help you learn how to use this software, as well as to help you visualize many
of the concepts taught in class.
Exams: All sections of Math 222 will take three common midterm
exams during the semester and one common final exam during the final exams
week. Midterm exams are held on Wednesdays on the following days:
|
Exam
1 |
February 7, 2007 |
|
Exam
2 |
March 7, 2007 |
|
Exam
3 |
April 11, 2007 |
Day sections will have common examinations on the above listed dates from 4:15pm to 5:40pm and evening sections from 5:45pm to 7:10pm. A comprehensive final examination will be given at the end of the semester. The date for this final examination will be announced at the end of the semester.
Attendance and Participation: Students must attend all classes. Absences from class will inhibit your ability to fully participate in class discussions and problem solving sessions and, therefore, affect your grade. Tardiness to class is very disruptive to the instructor and students and will not be tolerated.
Makeup Exam Policy: There will be no makeup exams, except in rare situations where the student has a legitimate reason for missing an exam, including illness, death in the family, accident, requirement to appear in court, etc. The student must notify the Math office and the Instructor that he/she will miss an exam. In all cases, the student must present proof for missing the exam, e.g., a doctor's note, police report, court notice, etc., clearly stating the date AND times.
Cellular Phones: All cellular phones and beepers must be switched off during all class times.
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Section & Topic |
Homework Assignments: |
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Week 1 (1/16 – 1/19) |
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1.1: |
Some Basic Math Models;
Direction Fields |
1 |
p. 7: |
7,10,15,16 |
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1.2: |
Solutions of Some Differential
Equations |
2 |
p.15: |
7,9,10,15 |
|
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1.3: |
Classification of Differential
Equations & |
3 |
p.24: |
1,2,5,8,12,14,17,18 |
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Week 2
(1/22 - 1/26) |
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2.1: |
Integrating Factors (cont.) |
4 |
p.39: |
1c,3c,7c,13,17,18,20 |
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2.2: |
Separable Equations |
5 |
p.47: |
1,2,3,7,10a,12a |
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2.4: |
Differences Between Linear and
Nonlinear Equations |
6 |
p.75: |
1,2,3,6,7,10,11 |
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Week 3 (1/29 - 2/2) |
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2.4: |
Differences Between Linear and Nonlinear
Equations (cont.) and Homogeneous Equations with Constant Coefficients |
7 |
p.142: |
1,3,6,8,9,10,12,16 |
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3.1: |
Constant Coefficients (cont.) |
8 |
p.142: |
17,18,
21,22 |
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2.7: |
Euler's Method |
9 |
☑ |
Study
for EXAM I |
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Week 4 (2/5 - 2/9) |
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☑
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REVIEW FOR EXAM I ~ 02/07/07 |
10 |
☑ |
Study for EXAM I |
|
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◄ COMMON EXAM I:
February 7, 2007 ► |
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3.2: |
Fundamental Solutions of Linear
Homogeneous Equations |
11 |
p.151: |
1,2,4,7,8,13,17 |
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☑
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GO OVER EXAM I |
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3.2: |
Fundamental Solutions of Linear
Homogeneous Equations (cont.) |
12 |
p.151: |
23,24,25 |
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Week 5 (2/12 - 2/16) |
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3.3: |
Linear Independence and the Wronskian |
13 |
p.158: |
2,4,5,6,9,10 |
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3.4: |
Complex Roots of the Characteristic
Equation |
14 |
p.164: |
3,4,7,9,10,13,17,18,19 |
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3.5: |
Repeated Roots; Reduction of
Order |
15 |
p.172: |
1,5,6,7,8,10,12,13 |
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Week 6 (2/19 - 2/23) |
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3.5: |
Repeated Roots; Reduction of
Order (cont.) |
16 |
p.172: |
23,25,26,27,28,30 |
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3.6: |
Nonhomogeneous Equations; Undetermined Coefficients |
17 |
p.184: |
1,3,4,6,8,12 |
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3.6: |
Nonhomogeneous Equations; Undetermined Coefficients (cont.) |
18 |
p.184: |
13,15,16,17,18 |
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Week 7 (2/26 - 3/2) |
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3.7: |
Variation of Parameters |
19 |
p.190: |
1,2,5,7,10 |
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3.7: |
Variation of Parameters (cont.) |
20 |
p.190: |
13,14,15,17,18 |
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4.2- |
Higher Order Linear Equations |
21 |
p.230: |
11,14; |
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Week 8
(3/5 - 3/9) |
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☑
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REVIEW FOR EXAM II ~ 03/07/07 |
22 |
☑ |
Study for EXAM II |
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◄ COMMON EXAM II:
March 7, 2007
► |
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3.8: |
Mechanical And Electrical
Vibrations |
23 |
p.203: |
1,2,6,7,11,14,15 |
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☑
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GO OVER EXAM II |
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3.8: |
Mechanical And Electrical
Vibrations (cont.) & |
24 |
p.203: |
17,18,19,20,24 & |
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Week 9
(3/12 - 3/16) |
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◄ SPRING RECESS:
March 12-16, 2007 ► |
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Week 10 (3/19 - 3/23) |
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6.1: |
Definition of the |
25 |
p.312: |
1,2,5,6,8,12,13,15,16 |
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6.1: |
Definition of the |
26 |
p.312: |
19,21,22 & |
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6.2: |
Solution of Initial Value Problems
(cont.) |
27 |
p.322: |
11,12,21,22,23,24 |
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Week 11 (3/26 – 3/30) |
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☑
|
MARCH 26, 2007: LAST DAY
TO WITHDRAW FROM THIS COURSE |
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6.3: |
Step Functions |
28 |
p.239: |
1,3,7,9,13,14,15 |
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6.4: |
Differential Equations with Discontinuous
Forcing Functions |
29 |
p.337: |
1,3,5 |
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6.4: |
Differential Equations with
Discontinuous Forcing Functions (cont.) |
30 |
p.337: |
6,7,9 |
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Week 12 (4/2 - 4/6) |
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6.5: |
Impulse Functions |
31 |
p.344: |
1,2,5,6 |
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6.6: |
The Convolution Integral |
32 |
p.351: |
4,6,8,9,13,14,17 |
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☑
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APRIL 6, 2007: GOOD
FRIDAY – NO CLASSES SCHEDULED |
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Week 13 (4/9 - 4/13) |
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☑
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REVIEW FOR EXAM III ~ 04/11/07 |
33 |
☑ |
Study for EXAM III |
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◄ COMMON EXAM III:
April 11, 2007
► |
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7.1: |
Introduction & |
34 |
p.360: |
2, 4, 5 & |
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☑
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GO OVER EXAM III |
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7.3: |
Linear Algebraic Equations; LI,
Eigenvalues, Eigenvectors |
35 |
p.383: |
15,16,18 |
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Week 14 (4/16 - 4/20) |
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7.5: |
Homogeneous Linear Systems with
Constant Coefficients |
35 |
p.398: |
1,4,7,9,10,15,16 |
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7.6: |
Complex Eigenvalues |
37 |
p.410: |
2,3,9,11,13,28 |
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10.1: |
Two-Point Boundary Value
Problems |
38 |
p.575: |
1,3,5,8,10,14,16,18 |
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Week 15 (4/23 - 4/27) |
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10.2: |
Fourier Series |
39 |
p.585: |
1,3,4,6,10,13,14,16,20,21 |
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10.4: |
Even and Odd Functions |
40 |
p.600: |
1,2,4,7,8 |
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10.4: |
Even and Odd Functions (cont.) |
41 |
p.600: |
17,18,20,21 |
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Week 16 (4/30- 5/1) |
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☑
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MAY 1, 2007: Classes
Follow a Friday Schedule |
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☑
|
REVIEW FOR FINAL
EXAM |
|
☑ |
Study
for FINAL |
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Final Exam
Week |
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FINAL EXAM WEEK:
May 3-9, 2007 |
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Prepared By: Prof. John Bechtold
Last
revised: December 6, 2006
U: 01/29/07
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January 15 |
M |
MLK
Day – No Classes Scheduled |
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March 26 |
M |
Last Day to Withdraw from Classes |
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April 6 |
F |
Good
Friday – No Classes Scheduled |
|
May 1 |
T |
Classes Follow a Friday
Schedule |